''Plus-Minus'', 2 × 7 pages for realisation, is a composition for one or several performers by

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th-century classical music, 20th and early 21st-century ...

, first written in 1963 and redrafted in 1974. It is Nr. 14 in the composer's catalogue of works, and has a variable performing length that depends on the version worked out from the given materials. The score is dedicated to

Mary Bauermeister Mary Hilde Ruth Bauermeister (born 7 September 1934) is a German artist who works in sculpture, drawing, installation, performance, and music. Influenced by Fluxus artists and Nouveau Réalisme, her work addresses esoteric issues of how informati ...

History

''Plus-Minus'' is a " polyvalent process composition", designed as a project for the composition students attending the first Cologne Courses for New Music, held at the in October to December 1963. In it, various compositional premises of Stockhausen's are presented in such a way as to enable the most radically different concrete results. ''Plus-Minus'' was composed in September 1963 while Stockhausen was in

Siculiana Siculiana is a town and ''comune'' in the province of Agrigento, Sicily, southern Italy, west of the provincial capital Agrigento. Geography Siculiana’s long coast line is largely unspoiled; a protected Regional Nature Reserve has been e ...

, preparing for what proved to be an aborted performance of ''

Momente ''Momente'' (Moments) is a work by the German composer Karlheinz Stockhausen, written between 1962 and 1969, scored for solo soprano, four mixed choirs, and thirteen instrumentalists (four trumpets, four trombones, three percussionists, and two e ...

'' at the Palermo Festival: The piece represents an extreme instance of the new, open type of composition Stockhausen was developing at the time, and evolved from a number of conversations with Mary Bauermeister in Siculiana and Palermo. Stockhausen's intention was to enable a music that reproduces itself, within a strict framework. Twenty-five different versions were made by the students in 1963, for a wide variety of forces: one for four harps, one for three harps and two pianos, one for recorders and children's choir, one for large orchestra, one for percussion and piano, one for two percussionists, and another for choir and chamber orchestra. The first public performance was given in Rome in June 1964 by

Cornelius Cardew Cornelius Cardew (7 May 193613 December 1981) was an English experimental music composer, and founder (with Howard Skempton and Michael Parsons) of the Scratch Orchestra, an experimental performing ensemble. He later rejected experimental music, ...

and

Frederic Rzewski Frederic Anthony Rzewski ( ; April 13, 1938 – June 26, 2021) was an American composer and pianist, considered to be one of the most important American composer-pianists of his time. His major compositions, which often incorporate social an ...

, each of whom realised one page of the score. When Stockhausen heard a tape of this performance, he was astonished that sounds he had usually avoided were being employed, exactly according to the score's specifications, to achieve a highly poetic quality.

Analysis

The course of the work is based on polarities of attraction and repulsion, of growth and decay. Material is systematically accumulated and eroded, in a process resembling a game of

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...

, where central and secondary notes either expand and proliferate, or are reduced until they disappear. These oppositions include, for example, the confrontation of materials having

definite pitch Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodie ...

with others of indeterminate pitch. The score systematically catalogues its materials into: # Seven types of events # Seven different ways of placing ornaments relative to a central sound (1) before, (2) simultaneous, (3) after, (4) before ''and'' after, (5) simultaneous ''and'' after, (6) before ''and'' simultaneous, (7) all three # Seven different formal units of the piece # Seven different basic types of grouping notes # Seven possible formal constellations for one complete realisation of seven formal units # Seven possible temporal combinations of adjacent events # Three types of rests separating events (long, medium, short) # Three types of superimposition # Seven possible overall characteristics of a given layer, (1) pitched sound, (2) noise (3–6) mixed pitch and noise (each one hard or soft), or (7) free There are seven so-called "symbol pages", on which all musical events are represented by

ideogram An ideogram or ideograph (from Greek "idea" and "to write") is a graphic symbol that represents an idea or concept, independent of any particular language, and specific words or phrases. Some ideograms are comprehensible only by famili ...

s, and a second set of "note pages" on which the pitch material for the events is notated. One or several layers of events can be worked out from these fourteen pages, and be combined according to particular rules. The note material is all derived from the prime and inverted forms of the following

twelve-tone row In music, a tone row or note row (german: Reihe or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets ar ...

: The types wax or wane according to the prescribed plus and minus processes, up to a maximum value of +13, which can result in very long sounds. If a process of diminution continues after reaching a value of 0, the events become represented by a "negative band of sound"—a "sound wall" of noise, such as breathing or radio noise, out of which silent events are cut until a value of −13 is reached, which is total silence. At that point, the event-type in question "dies" and may not be used again in the piece.

Reception

The score of ''Plus-Minus'' is complicated, delivering the message that composing

serial music In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were als ...

is hard work. The openness of the score was itself seen at the end of the 20th century as a form of control, deterring all but the most committed musicians from undertaking performances. Nevertheless, anyone making a realisation does have considerable control over the nature of the piece, and "negative-minded realisers can kill the piece, the over-positive can encourage disproportionate growth". At the first Cologne Courses, a student composer from Iceland, Atli Heimir Sveinsson, "assassinated" ''Plus-Minus'' by deliberately discovering the quickest way to end the piece. According to Stockhausen, "There were just a few blips and blobs and then lots of silences … that was it".

Discography

* ''Karlheinz Stockhausen: Piano Music''. Elisabeth Klein (piano); Stockhausen: '' Tierkreis'', '' Klavierstücke V'', ''IX'', and ''XI'' (two versions), ''Litanei'' from '' Aus den sieben Tagen'' (collage version of fragments from piano compositions by Stockhausen put together by Elisabeth Klein), A One-Page Version of Karlheinz Stockhausen's ''Plus-Minus'' (1963) for Solo Piano (1998), by Nils Holger Petersen. Recorded in the Levin Salen at the Norwegian State Academy of Music on August 14–15, 1998. CD recording. Classico CLASSCD 269. Frederiksberg, Denmark: Olufsen Records, 1999. Reissued in the Scandinavian Classics series as TIM 220555-205. Hamburg, Germany: TIM The International Music Company AG, 2002. *''Charlotte Moorman, Cello Anthology''.

Charlotte Moorman Madeline Charlotte Moorman (November 18, 1933 – November 8, 1991) was an American cellist, performance artist, and advocate for avant-garde music. Referred to as the "Jeanne d'Arc of new music", she was the founder of the Annual Avant Garde Fes ...

(cello),

Nam June Paik Nam June Paik (; July 20, 1932 – January 29, 2006) was a Korean American artist. He worked with a variety of media and is considered to be the founder of video art. He is credited with the first use (1974) of the term "electronic super h ...

(piano and Robot K-456),

Terry Jennings Terry Jennings (19 July 1940 – 11 December 1981) was an American minimalist composer and performer. Early life in California Terry Jennings was born in Eagle Rock, Los Angeles, California, in 1940. Coming from a background in jazz, he pla ...

(soprano saxophone), Benjamin Patterson,

Philip Corner Philip Lionel Corner (born April 10, 1933; name sometimes given as Phil Corner) is an American composer, trombonist, alphornist, vocalist, pianist, music theorist, music educator, and visual artist. Biography After The High School of Music & Ar ...

Malcolm Goldstein Malcolm Goldstein (born March 27, 1936 in Brooklyn, New York) is an American-Canadian composer, violinist and improviser who has been active in the presentation of new music and dance since the early 1960s. He received an M.A. in music compositio ...

Jackson Mac Low Jackson Mac Low (1922–2004) was an American poet, performance artist, composer and playwright, known to most readers of poetry as a practioneer of systematic chance operations and other non-intentional compositional methods in his work, which ...

David Behrman David Behrman (born August 16, 1937) is an American composer and a pioneer of computer music. In the early 1960s he was the producer of Columbia Records' ''Music of Our Time'' series, which included the first recording of Terry Riley's ''In C''. ...

Sylvano Bussotti Sylvano Bussotti (1 October 1931 – 19 September 2021) was an Italian composer of contemporary classical music, also a painter, set and costume designer, opera director and manager, writer and academic teacher. His compositions employ graphic n ...

: ''Sensitivo no. 7''; John Cage: ''26'1.1499"'' for a String Player (two versions);

Earle Brown Earle Brown (December 26, 1926 – July 2, 2002) was an American composer who established his own formal and notational systems. Brown was the creator of "open form," a style of musical construction that has influenced many composers since� ...

: ''November 1952'', ''December 1952'', and ''Synergy''; Terry Jennings: ''Piece for Cello and Saxophone''; Giuseppe Chiari: ''Per arco'', ''Ave Maria di Schubert''; Jackson Mac Low: ''Long Hot Summer''; Nam June Paik: Cello Sonata, opus 69; Sonata no. 1 for Adults Only, ''TV Cello Duets''; ''Concerto for TV Cello and Videotapes'', ''Waiting for Commercials''; Karlheinz Stockhausen: ''Plus-Minus'' (realisation by Nam June Paik with Robot K-456, aka Robot Opera); Toshi Ichiyanagi: Duet II. Charlotte Moorman interview by Harvey Matusow, BBC New York Studios, October 1969. Recorded between 1964 and 1982 in various locations (''Plus-Minus'' recorded in Judson Hall, New York City, Fall 1964). Compact disc 4 sound discs (digital, stereo, 4¾ in.) Alga Marghen 27NMN.064. Italy: Alga Marghen, 2006. Disc with ''Plus-Minus'' also issued separately, as ''Charlotte Moorman, Cello Anthology: Vol. 1''. Alga Marghen plana-M 27NMN.064.1. Italy: Alga Marghen, 2006. * ''Karlheinz Stockhausen: Plus-Minus''. Ives Ensemble. Stockhausen: '' Refrain'', ''

Kreuzspiel (Crossplay) is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951 (it was later revised for just three percussionists, along with other changes). It is assigned the number 1/7 in the comp ...

'', ''Plus-Minus'' (realisation by Christopher Fox and John Snijders). Recorded 29 June – 2 July 2002 at Theater Romein, Leeuwarden, Netherlands. CD recording. Hat Hut hat owRT 178. Basel, Switzerland: Hat Hut, 2010. * ''Ming Tsao: Plus Minus & Mirandas Atemwende''. ensemble ascolta. ''Plus-Minus'' (realisation by Ming Tsao). Ensemble ascolta;

Johannes Kalitzke Johannes Kalitzke (born 12 February 1959) is a German composer and conductor. After studying in Cologne and at the IRCAM in Paris, he was chief conductor at the Musiktheater im Revier in Gelsenkirchen for several years, then led the ensemble musi ...

(cond.). Recorded 18–19 July 2014, KvB-Saal Funkhaus Köln, Germany. CD recording, 1 disc: digital, stereo, 4¾ in. Vienna, Austria: Kairos, 2017.

References

Cited sources

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External links

Stockhausen: Sounds in Space – ''Plus-Minus''
analysis, Ed Chang {{Authority control Compositions by Karlheinz Stockhausen Chamber music by Karlheinz Stockhausen 20th-century classical music 1963 compositions Music dedicated to students or teachers Serial compositions Process music pieces Siculiana